1. Field of the Invention
The present invention is related to the field of transconductance cells, and more particularly, to multi-tanh doublet transconductance cells using emitter resistors.
2. Description of the Related Art
The output of a differential pair of common-emitter bipolar junction transistors (BJTs) has a hyperbolic tangent (tanh) type response to the input voltage applied between the base terminals. If this input base voltage is offset, the tanh function is also offset along the input voltage axis. Bipolar transistor cells which combine a number of offset tanh functions from a number of differential pairs of transistors are known as "multi-tanh" cells. By using at least two pairs of transistors, each with a different base offset voltage, a multi-tanh cell splits the individual transconductance functions of the differential pairs. Accordingly, the overall transconductance of the composite cell, achieved by summing the individual current outputs in phase, is more nearly linear, thereby allowing the cell to handle larger voltage swings at its input. FIG. 1 is a circuit diagram of a prior art multi-tanh cell that uses two differential pairs of BJTs, namely Q1-Q2 and Q3-Q4. Each pair is biased by a current source that supplies a bias current I.sub.T, which is also known as a tail current. Transistors Q2 and Q3 are fabricated with unit emitter areas "e", while transistors Q1 and Q4 are fabricated with emitter areas "Ae", that is, "A" times the emitter area of transistors Q2 and Q3. The cell of FIG. 1 will be referred to herein as a simple multi-tanh doublet.
The input base voltage of the left pair Q1-Q2 is offset from zero by an offset voltage V.sub.OS in one direction, while the input base voltage of the right pair Q3-Q4 is offset from zero by V.sub.OS in the other direction. The offset voltage is given by: EQU V.sub.OS =V.sub.T ln A (Equation 1)
where V.sub.OS is the offset voltage, A is the emitter area ratio, and V.sub.T is the thermal voltage (about 26 mVP, where "P" denotes "PTAT" or Proportional To Absolute Temperature with a reference temperature of about 300K). Although the input offset voltage is introduced through the use of the emitter area ratio A in the circuit of FIG. 1, other techniques can be used to generate the input offset voltage.
FIG. 2 is a graph showing the transconductance functions of the left pair (g.sub.m1) and the right pair (g.sub.m2) as a function of input base voltage for the circuit of FIG. 1. The functions have peaks that are laterally offset along the input base voltage (horizontal) axis from zero by -V.sub.OS and +V.sub.OS respectively.
FIG. 2 also shows the transconductance of the overall cell (g.sub.m), obtained by summing g.sub.m1 and g.sub.m2. As can be seen, the overall transconductance is nearly linear over a much wider range of input voltages (2.times.V.sub.OS) than available with either one of the differential pairs.
If the emitter area ratio is changed, then V.sub.OS is also changed according to Equation 1 above. This moves the transconductance curves of g.sub.m1 and g.sub.m2 laterally, and thus, also affects their sum g.sub.m. If V.sub.OS is too low, g.sub.m1 and g.sub.m2 will be too close, and g.sub.m will have a hump at V.sub.IN =0. If V.sub.OS is too high, g.sub.m1 and g.sub.m2 will be too far apart, and g.sub.m will have two humps with a valley in the middle where V.sub.IN =0.
There is only one value of the emitter area ratio A where linearity of g.sub.m will be optimized, i.e. which minimizes distortion of the dynamic range. That value is found to be A=A.sub.0 =3.732, and is the case plotted in FIG. 2.
Applying Equation 1 for A=A.sub.0 gives V.sub.OS =34.17 mVP. Accordingly, the doublet of FIG. 1 can provide linear transconductance over an input voltage swing of about 2.times.34.17 mV=68.34 mV. Although larger input voltage swings are often desirable, this limitation is fundamental to the simple doublet cell of FIG. 1. It can not be overcome by merely increasing A, since first, this would introduce distortion, as said above; second, there would be diminishing returns, since V.sub.OS increases only logarithmically with A as seen from Equation 1; and third, making the emitter areas larger would scale the device size, which would increase the undesirable junction capacitances.
Accordingly, a need remains for a doublet cell with a transconductance function exhibiting substantially perfect linearity over a a wide input voltage range.